A point object is placed at a distance of 15 cm from a convex lens of unknown focal length. A concave mirror of focal length 10 cm is placed 30 cm behind the lens, coaxial with it. It is observed that the light rays retrace their path after reflection from the mirror, such that the final image coincides with the object. The focal length of the convex lens is:

Step-by-step solution

For the light rays to retrace their path after reflection from the concave mirror, they must strike the mirror normally. This implies that the rays must appear to come from the center of curvature of the concave mirror. The radius of curvature of the concave mirror is R = 2f_m = 2 10 cm = 20 cm . Thus, the convex lens must form the first image of the object at the center of curvature of the mirror, which is 20 cm in front of the mirror. Given the distance between the lens and the mirror is 30 cm , the image distanc